This report better show the consumer is stepping up

After a surprisingly weak first-quarter GDP, investors will be scrutinizing May personal consumption data Thursday for signs the first quarter's weakness is well over.

Stocks trudged higher Wednesday, even after the final revision to first quarter GDP showed a stunning 2.9 percent decline, the worst since the great recession five years ago. Bond yields slid as investors moved into Treasurys. The 10-year note yield was as low as 2.52 percent but was at 2.55 percent in late trading.

The Dow gained 49 points, to 16,867 and S&P 500 rose 9 points, to 1,959, as equity investors shrugged off the report of economic activity for the winter months. Winter weather was to blame, but the latest revision came from a hit to consumer spending and a decline in exports.

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Personal income and spending data is released at 8:30 a.m. Thursday, at the same time as weekly jobless claims data. There is also the PCE deflator data, watched by the Fed as its preferred measure of inflation.

"We're going to get more detail about a very muddled picture. That has the potential to take the attention tomorrow," said Tom Simons, money markets economist at Jefferies.

"What we're thinking about the second-quarter growth rate, alto of it is going to depend on how much we get a bounce back in PCE," he said.

Some economists predicted a bigger second-quarter bounce back than initially expected, on the back of the first-quarter decline. CNBC's quick analysis of economists showed an expectation of 3.3 percent growth rate for the second quarter.

Economists pointed to a hit to health-care spending for the drop in consumption in the revised number. Credit Suisse said the health-care spending was reported to be adding 1 percent to growth, one of the largest increases in decades, but it was revised to negative 0.2 percentage points, an unusually weak number.

The calculations were based on assumptions about the Affordable Care Act's impact on spending that did not materialize.

"The Q1 shortfall would seem to leave room for a bigger snapback at first blush, although we would prefer to see that in the "hard" expenditure-side growth data before changing our estimates," the Credit Suisse economists wrote. They noted their second half forecast has GDP growing 2.5 to 3 percent.

Simons said his forecast is above the 0.4 percent consensus for spending, at 0.5 percent and he expects the core PCE (personal consumption expenditures) deflator at 0.2 percent.

"I don't see why anyone would think the economy is worse than it was 24 hours ago," he said.

Markets have been sensitive to inflation data, after CPI rose more than expected last week. Fed Chair Janet Yellen, during a press briefing, dismissed the move as "noise," so the PCE data is being closely watched by traders.

Jack Ablin, CIO of BMO Private Bank, said the Fed now may see its economic forecasts as too high, after a revised forecast was released last week.

"Instead of having a reasonable chance of exceeding 3 percent growth for the year, that's a high bar now that we've had one quarter where we dug a big hole. I'm hopeful to have a huge rebound. It leaves the Fed in an awkward spot. It's been forecasting much stronger economic activity all along the way, and they've been disappointed," he said. "I wouldn't be surprised if we saw some inflation pressure. Wages are starting to tighten up a little bit and housing I think, I'm looking at apartment rents are rising pretty steadily."

Ablin said the disappointment isn't enough to make him sell stocks, though he expects foreign markets to take over leadership. "I'm going to hold my nose and stay in," he said. "You've got pretty big hitters still bullish out there. Anecdotally things sound pretty good."

He said if there was some increase in inflation it could be a good sign for stocks, giving corporations pricing power and lifting revenues.

What to Watch

It could be a big day for IPOs Thursday, as GoPro, the maker of wearable HD action cameras, is expected to start trading. Michaels, the craft store, is expected to price Thursday and begin trading Friday.